56 ELECTRIC LIGHTING. 



the induced wire would be expressed by a quantity variable 

 no doubt with the machines, but which may, with the Alliance 

 machines, be six times greater than its true value. It follows 

 then, that, taking into account this increase ot resistance, 

 this work is proportional to the square of the electro-motive 

 force developed, and to the resistance of the external circuit, 

 and is inversely proportional to the square of the total re- 

 sistance of the circuit, and this leads to the conclusion 

 that the maximum effect is obtained when the resistance of 

 the external circuit exceeds that of the induced circuit by 

 the quantity with which this last must be increased in order 

 that Ohm's formula may be applicable to these machines. 



We shall not speak of the laws relating to induced currents 

 of different orders, for we shall have to concern ourselves but 

 little about these effects in the machines used for electric 

 lighting. But we must carefully study the influence on the 

 induced currents of the shape, the dimensions, and the com- 

 position of the magnetized core, as well as that which results 

 from the speed ot the alternate magnetizations and demag- 

 netizations. 



If it is considered that the power of electro-magnets is 

 proportional to the diameters of the magnetic cores, and to 

 the square root of their length, it may be supposed that it 

 would be of advantage to make the iron cores of induction 

 apparatus the thickest and the longest possible. But as the 

 alternations of magnetization and demagnetization are pro- 

 duced much more slowly with large iron cores than with small 

 ones, and as again a cylindrical metallic surface allows of the 

 formation of local induced currents which are developed to 

 the prejudice of the induced currents themselves, some 

 middle course had to be sought for, and recourse was had to 

 bundles of iron wires or of juxtaposed thin plates of sheet- 

 iron, the magnetic adherence of which is not sufficiently perfect 

 to be equivalent to a continuous mass of that metal. This 

 means has yielded excellent results, as we shall farther on 

 have occasion to observe. 



